Yes, Mr Cruz was a citizen of the US at his birth and thus was naturally born as a US citizen. He never was an “alien” and never was in need of naturalization and he never immigrated.
I would also point out that in Title 8 section 1401 section A, anyone born in the US is defined by law as “citizen”.
Remove that statute - POOF! No more citizenship.
You read words into the law that are not there.